Solving the Equation (x+3)² = 5
This equation involves a squared term, which means we'll need to use the square root to solve for x. Let's break down the steps:
1. Isolate the Squared Term

Take the square root of both sides: This will remove the square from the left side of the equation.
√((x+3)²) = ±√5

Simplify: Remember that taking the square root of a squared term results in the absolute value.
x+3 = ±√5
2. Solve for x

Consider both positive and negative roots: Because we took the square root, we need to account for both the positive and negative values of √5.
 Case 1: x + 3 = √5
 Case 2: x + 3 = √5

Solve for x in each case:
 Case 1: x = √5  3
 Case 2: x = √5  3
3. Solutions
Therefore, the solutions to the equation (x+3)² = 5 are:
 x = √5  3
 x = √5  3
These are the exact solutions. If you need an approximate decimal representation, you can use a calculator to evaluate these expressions.